Weighted Least Squares: an introduction

This video provides an introduction to Weighted Least Squares, and provides some insight into the intuition behind this estimator. Check out ben-lambert.com/econometrics-... for course materials, and information regarding updates on each of the courses. Quite excitingly (for me at least), I am about to publish a whole series of new videos on Bayesian statistics on youtube. See here for information: ben-lambert.com/bayesian/ Accompanying this series, there will be a book: www.amazon.co.uk/gp/product/1...

[@Gamabunta24345]

I keep coming back to your videos for so many of my classes. Thank you so much for having them! Huge help!

[@SpartacanUsuals]

Glad to hear you liked it! If you have any ideas for further videos then please let me know. Thanks, Ben

[@indrajeetjaveri3]

7:21 That was such an amazing intuitive(geometric) explanation of how exactly OLS & WLS differ fundamentally and you did it without first telling any math or stats behind it. Now looking at the math behind it would be so much easier knowing this. This reminds me of Grant Sanderson from 3Blue1Brown. Even he does intuitive explanations first and maths later. Thank you so much for this and please posting more such videos!

[@programacaosimples]

You are a great inspiration for me Ben! I love econometrics and the simple way you teach people. I am currently trying to teach how to perform econometrics in R for portuguese speakers, but, unfortunately, this is not a very popular topic in YT 😅

[@jakobforslin6301]

You deserve a medal!

[@xintongliu7968]

Very clear！ Thank you！

[@cihangwang8044]

Amazing explanation.

[@samirasahly6703]

Thanks for the explanation

[@tianshiliao5372]

Nice explanation, ty

[@xinking2644]

GOOD EXPALIN! thanks for your brilliant job, it really helps a lot =)

[@EvaLaurenson]

very helpful

[@tsunetasora]

Thank you my midterm savior ^u^

[@tOnmey]

Nice tutorial

[@ticklemedaly]

Excellent tutorial! Perhaps labeling video numbers would aid in what video is next.

[@SpartacanUsuals]

Hi, many thanks for your message, and kind words. If you visit my youtube channel homepage you can find the videos ordered into playlists. Best, Ben

[@pablohernandezgomez531]

I love you. We all do!

[@Ana230509]

If you Please can you put an example with concrete values?
Thanks

[@TheDefaulterror]

This is my first youtube comment ever! Good job! Your tutorial video has been very helpful to me! Please keep it up!

[@SJ-hz7iu]

Nice tutorial.If my suggestion worth noting then please kindly mark some key words in the side of the video so that the viewers can get them correctly. Since english is not my native language it was a bit difficult to catch few key words in the beginning of the video, especially at the description of GLS. May be this can be helpful to all others as well.. But still it helped for what I was looking for..Thank you..

[@SpartacanUsuals]

Hi, thanks for your message. I do eventually want to try to transcribe these videos - it may take me some time, but I think it would certainly be useful. Best, Ben

[@rolandleudjou7040]

Shital Joshi! you are right. I am french-speaking. I appreciate very well all Ben's videos. These help me understand many concepts in Econometrics. I have downloaded all. If transcripts exist I think I will be a master in Econometrics. Thank you, Ben!!

[@duyuchilyang2091]

Is this aitken gls?

[@sum1sw]

Oh man. I'm sorry, but you lost me from the very beginning, but I still gave you a like. What I am interested in is, given a set of observations (Xobs, YObs), and estimated error in X and Y, usually called Sigma,x and Sigma,y. I want to arrive at a calculated set of Xcalc and Ycalc. If all my Sigma's are equal, I want to take an orthogonal line from each observation, find the intersection point with the curve (calculated from the initial estimates of alpha and beta). This gives me Xcalc and Ycalc, I can then proceed to minimize (Xobs-Xcalc)^2/Simga,x^2 + (Yobs-Ycalc)^2/Sigma,Y^2. As you can tell, I'm not talking about a straight line, I'm actually talking about a multivariable implicit function f(x,y,x) = 0. I figured out how to do it if all IF my sigmas are 1 (or equal). I'm trying to figure out how to implement the Sigmas in the calculation when they are NOT equal (or unity).
I started out by linearising my the implicit equation using Taylor series around the point X0, Y0, Z0 which gives
F(X,Y,Z) ~ f(X0, Y0, Z0) + dF/dX(X-X0) + dF/dY(Y-Y0) + dF/dZ(Z-Z0) Note that this is the equation of a plane, not a line.
A line from the observed data point (Xobs, Yobs, Zobs), orthogonal to the plane, and in parametric form, is
+ t
I can solve for t at the intersection point. But how do I adjust the slope of this line so I can take the errors (Sigmas in X, Y, and Z) into account ?
That's my problem for today.